Lie symmetry analysis, analytical solutions and conservation laws to the coupled time fractional variant Boussinesq equations

Abstract

In this paper, under the background of the Riemann–Liouville fractional differential, a series of investigation of the coupled time fractional variant Boussinesq equations was done. Firstly, the Lie point symmetries were obtained by using the Li symmetry method. The symmetry reductions is also derived ulteriorly. Secondly, the power series method and the invariant subspace method are employed to acquire exact solutions of the coupled time fractional variant Boussinesq equations. Finally, conservation laws are well constructed based on the Noether theorem. What is more, dynamic behavior of all these exact solutions of the equation is described with the value of α changing.